Question

The ratio of densities of nitrogen and oxygen is 14 : 16. The temperature at which the speed of sound in nitrogen will be same as that in oxygen at ${55}^{0}C$ is

• A. ${35}^{0}C$
• B. ${48}^{0}C$
• C. ${65}^{0}C$
• D. ${14}^{0}C$

Answer 1

The correct option is D ${14}^{0}C$

The velocity of the sound in nitrogen is given by:

$v=\sqrt{\frac{\gamma RT}{M}}$

$\Rightarrow \frac{T_N}{T_0}=\frac{M_N}{M_0}$

$\Rightarrow \frac{T_N}{273+55}=\frac{14}{16}=\frac{7}{8}$

Therefore, the temperature at which speed of nitrogen will be same as that of oxygen will be:

$\Rightarrow T_N=287K={14}^{\circ }C$